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Brass, Moser, and Pach call it "one of the oldest and most extensively studied geometric questions concerning lattice points". [1] At most points can be placed, because + points in a grid would include a row of three or more points, by the pigeonhole principle.
A gridshell is a structure which derives its strength from its double curvature (in a similar way that a fabric structure derives strength from double curvature), but is constructed of a grid or lattice. The grid can be made of any material, but is most often wood (similar to garden trellis) or steel.
Latticework may be functional – for example, to allow airflow to or through an area; structural, as a truss in a lattice girder; [2] used to add privacy, as through a lattice screen; purely decorative; or some combination of these. Latticework in stone or wood from the classical period is also called Roman lattice or transenna (plural transenne).
A common type of lattice graph (known under different names, such as grid graph or square grid graph) is the graph whose vertices correspond to the points in the plane with integer coordinates, x-coordinates being in the range 1, ..., n, y-coordinates being in the range 1, ..., m, and two vertices being connected by an edge whenever the corresponding points are at distance 1.
A lattice girder, like any girder, primarily resists bending. The component sections may typically include metal beams, channel and angle sections, with the lacing elements either metal plate strips, or angle sections. The lacing elements are typically attached using either hot rivets or threaded locator bolts.
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.
William Thurston () describes a test for determining whether a simply-connected region, formed as the union of unit squares in the plane, has a domino tiling.He forms an undirected graph that has as its vertices the points (x,y,z) in the three-dimensional integer lattice, where each such point is connected to four neighbors: if x + y is even, then (x,y,z) is connected to (x + 1,y,z + 1), (x ...
In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice (a lattice path) that does not visit the same point more than once. This is a special case of the graph theoretical notion of a path. A self-avoiding polygon (SAP) is a closed self-avoiding walk on a lattice. Very little is known rigorously about the self-avoiding ...
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